This research fellowship is not specifically an archives/RIM position, but could be of interest to persons in those fields.
Kew, Richmond, Surrey, UK: Archives Graduate Trainee, Kew Royal Botanic Gardens
Thanks to @DavidUnderdown9 for this one!
Atlanta, GA: Research Library Fellow, Emory University
Princeton, NJ: Summer Fellowship, Princeton University Mudd Library
Source: Thanks to Rachel for this one!
Salem, MA: 2015 Native American Fellowships, Peabody Essex Museum
Note: These summer fellowship opportunities for graduate students and cultural professionals of Native American, Native Hawaiian or Alaska Native background.
Link out to job announcement (Opens a PDF)
Source: A&A Listserv
Washington, DC: Junior Fellows, Library of Congress
Source: USAjobs
New Haven, CT: Kress Fellowship in Art Librarianship, Yale University
Source: ALA JobList
San Francisco, CA: Postdoc Visual Curation Fellow, Internet Archive
Source: Code4Lib
Newark, NJ: Inst. of Jazz Studies Fellowships, Rutgers University
Source: SAA Career Center
Raleigh, NC: Libraries Fellows, North Carolina State University
While this is not specifically an archives job, this may be of interest to recent and upcoming grads!
Source: University of Toronto iSchool
Archives Gig 